Ferromagnetic Liquid Research Articles

Evidence for dynamic kagome ice

The search for two-dimensional quantum spin liquids, exotic magnetic states remaining disordered down to zero temperature, has been a great challenge in frustrated magnetism over the last few decades. Recently, evidence for fractionalized excitations, called spinons, emerging from these states has been observed in kagome and triangular antiferromagnets. In contrast, quantum ferromagnetic spin liquids in two dimensions, namely quantum kagome ices, have been less investigated, yet their classical counterparts exhibit amazing properties, magnetic monopole crystals as well as magnetic fragmentation. Here, we show that applying a magnetic field to the pyrochlore oxide Nd2Zr2O7, which has been shown to develop three-dimensional quantum magnetic fragmentation in zero field, results in a dimensional reduction, creating a dynamic kagome ice state: the spin excitation spectrum determined by neutron scattering encompasses a flat mode with a six arm shape akin to the kagome ice structure factor, from which dispersive branches emerge.

Robust non-Abelian spin liquid and a possible intermediate phase in the antiferromagnetic Kitaev model with magnetic field

We investigate the non-Abelian topological chiral spin liquid phase in the two-dimensional (2D) Kitaev honeycomb model subject to a magnetic field. By combining density matrix renormalization group (DMRG) and exact diagonalization (ED) we study the energy spectra, entanglement, topological degeneracy, and expectation values of Wilson loop operators, allowing for robust characterization. While the ferromagnetic (FM) Kitaev spin liquid is already destroyed by a weak magnetic field with Zeeman energy $H_*^\text{FM} \approx 0.02$, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic field that is an order of magnitude larger, $H_*^\text{AFM} \approx 0.2$. Interestingly, for larger fields $H_*^\text{AFM} < H < H_{**}^\text{AFM}$, an intermediate gapless phase is observed, before a second transition to the high-field partially-polarized paramagnet. We attribute this rich phase diagram, and the remarkable stability of the chiral topological phase in the AFM Kitaev model, to the interplay of strong spin-orbit coupling and frustration enhanced by the magnetic field. Our findings suggest relevance to recent experiments on RuCl$_3$ under magnetic fields.

Universality and Quantum Criticality of the One-Dimensional Spinor Bose Gas.

We investigate the universal thermodynamics of the two-component one-dimensional Bose gas with contact interactions in the vicinity of the quantum critical point separating the vacuum and the ferromagnetic liquid regime. We find that the quantum critical region belongs to the universality class of the spin-degenerate impenetrable particle gas which, surprisingly, is very different from the single-component case and identify its boundaries with the peaks of the specific heat. In addition, we show that the compressibility Wilson ratio, which quantifies the relative strength of thermal and quantum fluctuations, serves as a good discriminator of the quantum regimes near the quantum critical point. Remarkably, in the Tonks-Girardeau regime, the universal contact develops a pronounced minimum, reflected in a counterintuitive narrowing of the momentum distribution as we increase the temperature. This momentum reconstruction, also present at low and intermediate momenta, signals the transition from the ferromagnetic to the spin-incoherent Luttinger liquid phase and can be detected in current experiments with ultracold atomic gases in optical lattices.

Application of the magnetic fluid as a detector for changing the magnetic field

In article the possibility of use of magnetic fluid as a sensitive element for fixing of change of induction of magnetic field in space is considered. Importance of solvable tasks is connected with search of the perspective magnetic substances susceptible to weak magnetic field. The results of a study of the capacitive method for fixing the change in the magnetic field on the basis of a ferromagnetic liquid are presented. The formation of chain structures in the ferrofluid from magnetic particles under the influence of the applied magnetic field leads to a change in the capacitance of the plate condenser. This task has important practical value for development of a magnetosensitive sensor of change of magnetic field.

Effects of flow on the dynamics of a ferromagnetic nematic liquid crystal.

We investigate the effects of flow on the dynamics of ferromagnetic nematic liquid crystals. As a model, we study the coupled dynamics of the magnetization, M, the director field, n, associated with the liquid crystalline orientational order, and the velocity field, v. We evaluate how simple shear flow in a ferromagnetic nematic is modified in the presence of small external magnetic fields, and we make experimentally testable predictions for the resulting effective shear viscosity: an increase by a factor of 2 in a magnetic field of about 20 mT. Flow alignment, a characteristic feature of classical uniaxial nematic liquid crystals, is analyzed for ferromagnetic nematics for the two cases of magnetization in or perpendicular to the shear plane. In the former case, we find that small in-plane magnetic fields are sufficient to suppress tumbling and thus that the boundary between flow alignment and tumbling can be controlled easily. In the latter case, we furthermore find a possibility of flow alignment in a regime for which one obtains tumbling for the pure nematic component. We derive the analogs of the three Miesowicz viscosities well-known from usual nematic liquid crystals, corresponding to nine different configurations. Combinations of these can be used to determine several dynamic coefficients experimentally.

Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals

Liquid crystals are widely known for their facile responses to external fields, which forms a basis of the modern information display technology. However, switching of molecular alignment field configurations typically involves topologically trivial structures, although singular line and point defects often appear as short-lived transient states. Here, we demonstrate electric and magnetic switching of nonsingular solitonic structures in chiral nematic and ferromagnetic liquid crystals. These topological soliton structures are characterized by Hopf indices, integers corresponding to the numbers of times that closed-loop-like spatial regions (dubbed "preimages") of two different single orientations of rod-like molecules or magnetization are linked with each other. We show that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices. The field transformations during such switching are continuous when Hopf indices remain unchanged, even when involving transformations of preimages, but discontinuous otherwise.

Magneto-optic dynamics in a ferromagnetic nematic liquid crystal.

We investigate dynamic magneto-optic effects in a ferromagnetic nematic liquid crystal experimentally and theoretically. Experimentally we measure the magnetization and the phase difference of the transmitted light when an external magnetic field is applied. As a model we study the coupled dynamics of the magnetization, M, and the director field, n, associated with the liquid crystalline orientational order. We demonstrate that the experimentally studied macroscopic dynamic behavior reveals the importance of a dynamic cross-coupling between M and n. The experimental data are used to extract the value of the dissipative cross-coupling coefficient. We also make concrete predictions about how reversible cross-coupling terms between the magnetization and the director could be detected experimentally by measurements of the transmitted light intensity as well as by analyzing the azimuthal angle of the magnetization and the director out of the plane spanned by the anchoring axis and the external magnetic field. We derive the eigenmodes of the coupled system and study their relaxation rates. We show that in the usual experimental setup used for measuring the relaxation rates of the splay-bend or twist-bend eigenmodes of a nematic liquid crystal one expects for a ferromagnetic nematic liquid crystal a mixture of at least two eigenmodes.

Director reorientation dynamics of ferromagnetic nematic liquid crystals.

Successful realization of ferromagnetic nematic liquid crystals has opened up the possibility to experimentally study a completely new set of fundamental physical phenomena. In this contribution we present a detailed investigation of some aspects of the static response and the complex dynamics of ferromagnetic liquid crystals under the application of an external magnetic field. Experimental results are then compared with a macroscopic model. Dynamics of the director were measured by optical methods and analyzed in terms of a theoretical macroscopic model. A dissipative cross-coupling coefficient describing the dynamic coupling between the two system order parameters, the magnetization and the nematic director, is needed to explain the results. In this contribution we examine the dependency of this coefficient on material parameters and the saturation magnetization and the liquid crystal host. Despite the complexity of the system, the theoretical description allows for a proper interpretation of the results and is connected to several microscopic aspects of the colloidal suspension.

Sorption of Rhenium from Concentration Products of Placers of Concentrate Gold by Magnetic Liquid Separation

Separation in ferromagnetic liquid (FML) is recommended for separating gold from concentration products of placers. Magnetic liquid separation is based on the appearance in FML of a ponderomotive force of a nonuniform magnetic liquid additional to the gravity buoyancy force. A horizontal component of this force in the separation medium bulk participates in the body motion along the equipotential surface across the working zone—to separation cuvette walls and towards the central plane of the pole gap, while the longitudinal component is directed along it. In order to increase process characteristics, it is recommended to limit transverse motions of bodies by vertical partitions established in the separation medium along the separator pole gap. It follows from the results of a theoretical investigation into the particle motion in a separator working zone that the influence of walls manifests itself in the appearance of the counterflow to the particle motion, which causes the rise of the hydrodynamic drag force and deceleration of the particle motion. It is shown that, in the presence of vertical walls, shortening the residence time of a light concentrate fraction in a separator working zone promotes the rise of process productivity in regards to the initial feed and productivity in regards to a heavy fraction (recovery of gold into the heavy fraction). Research tests of competitive separation methods for artificial mixtures of minerals and heavy gold-bearing concentrates are performed using methods of mathematical experiment design. It is proven that, when passing from separation in the FML volume to separation using the developed method, the apparatus productivity increases by 9%, while the recovery of gold into the heavy fraction increases from 84.34 to 91.77% due to a decrease in losses with a light fraction from 15.46 to 7.96%. The material containing gold in amounts more than 800 kg/t is acquired with a decrease in the yield of a heavy fraction by 11 rel. %.

Field-controlled structures in ferromagnetic cholesteric liquid crystals.

One of the advantages of anisotropic soft materials is that their structures and, consequently, their properties can be controlled by moderate external fields. Whereas the control of materials with uniform orientational order is straightforward, manipulation of systems with complex orientational order is challenging. We show that a variety of structures of an interesting liquid material, which combine chiral orientational order with ferromagnetic one, can be controlled by a combination of small magnetic and electric fields. In the suspensions of magnetic nanoplatelets in chiral nematic liquid crystals, the platelet's magnetic moments orient along the orientation of the liquid crystal and, consequently, the material exhibits linear response to small magnetic fields. In the absence of external fields, orientations of the liquid crystal and magnetization have wound structure, which can be either homogeneously helical, disordered, or ordered in complex patterns, depending on the boundary condition at the surfaces and the history of the sample. We demonstrate that by using different combinations of small magnetic and electric fields, it is possible to control reversibly the formation of the structures in a layer of the material. In such a way, different periodic structures can be explored and some of them may be suitable for photonic applications. The material is also a convenient model system to study chiral magnetic structures, because it is a unique liquid analog of a solid helimagnet.

Impact of Cattaneo-Christov Heat Flux Model on the Flow of Maxwell Ferromagnetic Liquid Along a Cold Flat Plate Embedded with Two Equal Magnetic Dipoles

The target of the current study is to inspect theoretically two-dimensional boundary layer flow of a Maxwell ferromagnetic fluid toward a flat plate. An external magnetic field due to two equal line dipole which are equidistant from the wall and perpendicular to the flow plane is applied. Cattaneo-Christov heat flux model is utilized in modified form of Fourier’s Law to disclose the heat transfer characteristic. Governing flow problem is normalized into ordinary differential equation by adopting similarity transform procedure. The solution of resulting non-linear ODE’s are solved by shooting technique based on Runge-Kutta algorithm with the help of MATLAB. Characteristic of sundry parameter like magneto-thermomechanical (ferrohydrodynamic) interaction parameter, dimensionless thermal relaxation, Prandtl number and Debora number on velocity and temperature profile are displayed via graphs and in tabular form. It is also pointed out that temperature profile suppresses by varying values of the thermal relaxation time and Prandtl number and increasing behaviour is seen against ferrohydrodynamic interaction. Present numerical results are compared with those published previously in the literature for the case of Newtonian fluid (α₁ → 0) and found an excellent agreement.

Dynamic Magneto-optic Coupling in a Ferromagnetic Nematic Liquid Crystal.

Hydrodynamics of complex fluids with multiple order parameters is governed by a set of dynamic equations with many material constants, of which only some are easily measurable. We present a unique example of a dynamic magneto-optic coupling in a ferromagnetic nematic liquid, in which long-range orientational order of liquid crystalline molecules is accompanied by long-range magnetic order of magnetic nanoplatelets. We investigate the dynamics of the magneto-optic response experimentally and theoretically and find out that it is significantly affected by the dissipative dynamic cross-coupling between the nematic and magnetic order parameters. The cross-coupling coefficient determined by fitting the experimental results with a macroscopic theory is of the same order of magnitude as the dissipative coefficient (rotational viscosity) that governs the reorientation of pure liquid crystals.

Detection of magnetized quark-nuggets, a candidate for dark matter

Quark nuggets are theoretical objects composed of approximately equal numbers of up, down, and strange quarks and are also called strangelets and nuclearites. They have been proposed as a candidate for dark matter, which constitutes ~85% of the universe’s mass and which has been a mystery for decades. Previous efforts to detect quark nuggets assumed that the nuclear-density core interacts directly with the surrounding matter so the stopping power is minimal. Tatsumi found that quark nuggets could well exist as a ferromagnetic liquid with a ~1012-T magnetic field. We find that the magnetic field produces a magnetopause with surrounding plasma, as the earth’s magnetic field produces a magnetopause with the solar wind, and substantially increases their energy deposition rate in matter. We use the magnetopause model to compute the energy deposition as a function of quark-nugget mass and to analyze testing the quark-nugget hypothesis for dark matter by observations in air, water, and land. We conclude the water option is most promising.

Application of immiscible magnetic liquids of different densities as the separation medium for magnetic liquid separation

Results of an investigation into a new method of magnetic liquid separation, which differs from known ones by the presence of a bilayer separation medium in the form of immiscible ferromagnetic liquids of different densities, are presented. During the separation in a bilayer medium, the equilibrium condition of a particle on a flat surface, which is written according to the Young law and Neumann rule, should be supplemented by the linear tension of a curve-phase interface surface. The linear tension is the force and energy barrier, which prevents fastening of small particles of precious metals at the phase interface, and the cause of their effective separation into a heavy fraction. The method of magnetic liquid separation is tested for concentrates containing platinum group metals. It is established that, during the separation in the bilayer medium, the recovery of platinum group metals into the heavy fraction is 25.89%, while that for the waterbased ferromagnetic liquid is 19.73%. The quality of the heavy fraction makes gives the opportunity to direct it to the hydrometallurgical stage bypassing the copper plant, which increases the recovery of precious metals by 5.0 abs %.

Thermal Convection in Variable Viscosity Ferromagnetic Liquids with Heat Source

A linear stability analysis of thermal convection in variable viscosity Newtonian ferromagnetic liquid by considering all possible boundary combinations is studied. The importance of this problem lies in the interesting possibility of regulating convection using heat source (sink). Using Galerkin technique the critical eigenvalue and wave number for stationary convection are obtained. These critical values are then improved upon by the shooting method. The influence of various parameters on the onset of convection has been analyzed.

Magnetic-field tuning of whispering gallery mode lasing from ferromagnetic nematic liquid crystal microdroplets.

We report magnetic field tuning of the structure and Whispering Gallery Mode lasing from ferromagnetic nematic liquid crystal micro-droplets. Microlasers were prepared by dispersing a nematic liquid crystal, containing magnetic nanoparticles and fluorescent dye, in a glycerol-lecithin matrix. The droplets exhibit radial director structure, which shows elastic distortion at a very low external magnetic field. The fluorescent dye doped ferromagnetic nematic droplets show Whispering Gallery Mode lasing, which is tunable by the external magnetic field. The tuning of the WGM lasing modes is linear in magnetic field with a wavelength-shift of the order of 1 nm/100 mT. Depending on the lasing geometry, the WGMs are red- or blue-shifted.

Interplay between exotic superfluidity and magnetism in a chain of four-component ultracold atoms

We investigate the spin-polarized chain of ultracold fermionic atoms with spin-3/2 described by the fermionic Hubbard model with SU(4) symmetric attractive interaction. The competition of bound pairs, trions, quartets and unbound atoms is studied analytically and by density matrix renormalization group simulations. We find several distinct states where bound particles coexist with the ferromagnetic state of unpaired fermions. In particular, an exotic inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type superfluid of quartets in a magnetic background of uncorrelated atoms is found for weaker interactions. We show that the system can be driven from this quartet-FFLO state to a molecular state of localized quartets which is also reflected in the static structure factor. For strong enough coupling, spatial segregation between molecular crystals and ferromagnetic liquids emerges due to the large effective mass of the composite particles.

Increasing the capabilities of machining attachments by means of ferromagnetic liquids

The article is devoted to application of ferromagnetic liquids in machining attachments of technical process for producing machine components. Application of such liquids allows to simplify equipment and decrease its cost, to increase accuracy of workpieces treatment by elimination of additional processing of workpieces base surfaces. It is proposed to set the workpiece not on supports of machine-tools but on the layer of rheological liquid hardened in outer magnetic field. At the same time contact pressure of rheological medium on side surface provides slip resistance caused by the forces appearing during treatment. The article contains calculated dependences for definition of forces holding the workpiece on machine table, being fully or partially submerged into ferromagnetic medium during mechanical processing. Criterion for applicability of ferromagnetic liquid at workpiece setting during treatment is proposed. On the ground of achieved per samples experimental verification of formulated statements and calculated dependences the authors worked out recommendations for selection of rheological media in liquid state for workpiece setting and holding taking into account frequent changes of working objects. Development and running of such machining attachments is efficient in modern industry that is characterized by low serial production and wide assortment of produced goods during finishing mechanical, electrical and combined work, where scientifically grounded application of ferromagnetic liquids increases production profitability by 1, 5-2 times.

Using immiscible magnetic liquids of different density as a separating medium for magnetic liquid separation

The article presents the results of a new magnetic liquid separation method study. This method differs from known methods by the presence of a bilayer separation medium in the form of immiscible ferromagnetic liquids of different density. When separating in a bilayer separation medium, the particle equilibrium condition on a plane surface, recorded according to Young's law and Neumann's rule, must be supplemented by the linear tension of a curved phase interface. A linear tension is a force and energy barrier that prevents fixing of fine particles of noble metals at the phase interface, and is the reason for their effective extraction into the heavy fraction. The magnetic liquid separation method was tested on concentrates containing platinoids. It was established that during separation in a bilayer medium, the extraction of platinoids into the heavy fraction was 25,89 %, and during separation in a water-based ferromagnetic fluid it was 19,73 %. The quality of the heavy fraction makes it possible to direct it to the hydrometallurgical process, bypassing the copper plant, which increases the extraction of precious metals by 5,0 % abs.

Effects of electric field on thermodynamics and ordering of a dipolar liquid.

We propose that an electric field's role in changing the structural disorder may be investigated by comparing the field-induced entropy decrease, ΔES, against the pressure-induced and cooling-induced entropy decreases, ΔpS and ΔTS, respectively, for the same increase in the dielectric α-relaxation time, Δτα, or in the viscosity. If these three quantities are found to be the same, the change in the number of microstates, Δln Ω = ΔS/R, would be the same whether there is an electric field-induced dipole vector alignment, or not. The available data [S. Samanta and R. Richert, J. Chem. Phys. 142, 044504 (2015)] show that ΔES ≅ ΔpS, and ΔES ≅ ΔTS. We further argue that in the case of conformational disorder without hydrodynamics, as for a flexible molecule's orientationally disordered or plastic crystal, ΔTS would be more negative than ΔES for the same increase in Δτα. For cyclo-octanol plastic crystal, whose octyl-ring would lose some of its dielectrically inactive conformational degrees of freedom on cooling, ΔTS is five-times ΔES. Hence the entropy of such crystals may not be related to their τα, an aspect relevant to certain biopolymer crystals. We also mention other effects of E. The findings are relevant to a number of recent studies on the analysis of the effect of electric field on a liquid's properties. The method can be used to study the role of other entropy-altering variables in liquid crystals and ferromagnetic liquids.